CopperSpice API  1.7.2
QTransform Class Reference

Specifies 2D transformations of a coordinate system. More...

Public Types

enum  TransformationType
 

Public Methods

 QTransform ()
 
 QTransform (const QMatrix &matrix)
 
 QTransform (qreal m11, qreal m12, qreal m13, qreal m21, qreal m22, qreal m23, qreal m31, qreal m32, qreal m33=1.0)
 
 QTransform (qreal m11, qreal m12, qreal m21, qreal m22, qreal dx, qreal dy)
 
QTransform adjoint () const
 
qreal det () const
 
qreal determinant () const
 
qreal dx () const
 
qreal dy () const
 
QTransform inverted (bool *invertible=nullptr) const
 
bool isAffine () const
 
bool isIdentity () const
 
bool isInvertible () const
 
bool isRotating () const
 
bool isScaling () const
 
bool isTranslating () const
 
qreal m11 () const
 
qreal m12 () const
 
qreal m13 () const
 
qreal m21 () const
 
qreal m22 () const
 
qreal m23 () const
 
qreal m31 () const
 
qreal m32 () const
 
qreal m33 () const
 
QLine map (const QLine &line) const
 
QLineF map (const QLineF &line) const
 
QPainterPath map (const QPainterPath &path) const
 
QPoint map (const QPoint &point) const
 
QPointF map (const QPointF &point) const
 
QPolygon map (const QPolygon &polygon) const
 
QPolygonF map (const QPolygonF &polygon) const
 
QRegion map (const QRegion &region) const
 
void map (int x, int y, int *tx, int *ty) const
 
void map (qreal x, qreal y, qreal *tx, qreal *ty) const
 
QRect mapRect (const QRect &rect) const
 
QRectF mapRect (const QRectF &rect) const
 
QPolygon mapToPolygon (const QRect &rect) const
 
 operator QVariant () const
 
bool operator!= (const QTransform &transform) const
 
QTransform operator* (const QTransform &transform) const
 
QTransform & operator*= (const QTransform &transform)
 
QTransform & operator*= (qreal factor)
 
QTransform & operator+= (qreal delta)
 
QTransform & operator-= (qreal delta)
 
QTransform & operator/= (qreal factor)
 
QTransform & operator= (const QTransform &other)
 
bool operator== (const QTransform &transform) const
 
void reset ()
 
QTransform & rotate (qreal angle, Qt::Axis axis=Qt::ZAxis)
 
QTransform & rotateRadians (qreal angle, Qt::Axis axis=Qt::ZAxis)
 
QTransform & scale (qreal sx, qreal sy)
 
void setMatrix (qreal m11, qreal m12, qreal m13, qreal m21, qreal m22, qreal m23, qreal m31, qreal m32, qreal m33)
 
QTransform & shear (qreal sh, qreal sv)
 
const QMatrixtoAffine () const
 
QTransform & translate (qreal dx, qreal dy)
 
QTransform transposed () const
 
TransformationType type () const
 

Static Public Methods

static QTransform fromScale (qreal sx, qreal sy)
 
static QTransform fromTranslate (qreal dx, qreal dy)
 
static bool quadToQuad (const QPolygonF &quad1, const QPolygonF &quad2, QTransform &result)
 
static bool quadToSquare (const QPolygonF &quad, QTransform &result)
 
static bool squareToQuad (const QPolygonF &quad, QTransform &result)
 

Related Functions

These are not member functions

QLine operator* (const QLine &line, const QTransform &matrix)
 
QLineF operator* (const QLineF &line, const QTransform &matrix)
 
QPainterPath operator* (const QPainterPath &path, const QTransform &matrix)
 
QPoint operator* (const QPoint &point, const QTransform &matrix)
 
QPointF operator* (const QPointF &point, const QTransform &matrix)
 
QPolygon operator* (const QPolygon &polygon, const QTransform &matrix)
 
QPolygonF operator* (const QPolygonF &polygon, const QTransform &matrix)
 
QRegion operator* (const QRegion &region, const QTransform &matrix)
 
QDataStreamoperator<< (QDataStream &stream, const QTransform &matrix)
 
QDataStreamoperator>> (QDataStream &stream, QTransform &matrix)
 
bool qFuzzyCompare (const QTransform &transform1, const QTransform &transform2)
 
uint qHash (const QTransform &key, uint seed=0)
 

Detailed Description

The QTransform class specifies 2D transformations of a coordinate system. A transformation specifies how to translate, scale, shear, rotate or project the coordinate system, and is typically used when rendering graphics. QTransform is a true 3x3 matrix, allowing perspective transformations.

QTransform's toAffine() method allows converting QTransform to QMatrix. If a perspective transformation has been specified on the matrix, then the conversion will cause loss of data.

A QTransform object can be built using the setMatrix(), scale(), rotate(), translate() and shear() functions. Alternatively, it can be built by applying Basic Matrix Operations. The matrix can also be defined when constructed, and it can be reset to the identity matrix (the default) using the reset() method.

The QTransform class supports mapping of graphic primitives: A given point, line, polygon, region, or painter path can be mapped to the coordinate system defined by this matrix using the map() function. In case of a rectangle, its coordinates can be transformed using the mapRect() function. A rectangle can also be transformed into a polygon (mapped to the coordinate system defined by this matrix), using the mapToPolygon() function.

QTransform provides the isIdentity() function which returns true if the matrix is the identity matrix, and the isInvertible() function which returns true if the matrix is non-singular (i.e. AB = BA = I). The inverted() function returns an inverted copy of this matrix if it is invertible (otherwise it returns the identity matrix), and adjoint() returns the matrix's classical adjoint. In addition, QTransform provides the determinant() function which returns the matrix's determinant.

Finally, the QTransform class supports matrix multiplication, addition and subtraction, and objects of the class can be streamed as well as compared.

Rendering Graphics

When rendering graphics, the matrix defines the transformations but the actual transformation is performed by the drawing routines in QPainter.

By default, QPainter operates on the associated device's own coordinate system. The standard coordinate system of a QPaintDevice has its origin located at the top-left position. The x values increase to the right; y values increase downward. For a complete description, see the coordinate system documentation.

QPainter has functions to translate, scale, shear and rotate the coordinate system without using a QTransform. For example:

void SimpleTransformation::paintEvent(QPaintEvent *)
{
QPainter painter(this);
painter.setPen(QPen(Qt::blue, 1, Qt::DashLine));
painter.drawRect(0, 0, 100, 100);
painter.rotate(45);
painter.setFont(QFont("Helvetica", 24));
painter.setPen(QPen(Qt::black, 1));
painter.drawText(20, 10, "QTransform");
}

Although these functions are very convenient, it can be more efficient to build a QTransform and call QPainter::setTransform() if you want to perform more than a single transform operation. For example:

void CombinedTransformation::paintEvent(QPaintEvent *)
{
QPainter painter(this);
painter.setPen(QPen(Qt::blue, 1, Qt::DashLine));
painter.drawRect(0, 0, 100, 100);
QTransform transform;
transform.translate(50, 50);
transform.rotate(45);
transform.scale(0.5, 1.0);
painter.setTransform(transform);
painter.setFont(QFont("Helvetica", 24));
painter.setPen(QPen(Qt::black, 1));
painter.drawText(20, 10, "QTransform");
}

Basic Matrix Operations

A QTransform object contains a 3 x 3 matrix. The m31 (dx) and m32 (dy) elements specify horizontal and vertical translation. The m11 and m22 elements specify horizontal and vertical scaling. The m21 and m12 elements specify horizontal and vertical shearing. And finally, the m13 and m23 elements specify horizontal and vertical projection, with m33 as an additional projection factor.

QTransform transforms a point in the plane to another point using the following formulas:

x' = m11*x + m21*y + dx
y' = m22*y + m12*x + dy
if (is not affine) {
w' = m13*x + m23*y + m33
x' /= w'
y' /= w'
}

The point (x, y) is the original point, and (x', y') is the transformed point. (x', y') can be transformed back to (x, y) by performing the same operation on the inverted() matrix.

The various matrix elements can be set when constructing the matrix, or by using the setMatrix() function later on. They can also be manipulated using the translate(), rotate(), scale() and shear() convenience functions. The currently set values can be retrieved using the m11(), m12(), m13(), m21(), m22(), m23(), m31(), m32(), m33(), dx() and dy() functions.

Translation is the simplest transformation. Setting dx and dy will move the coordinate system dx units along the X axis and dy units along the Y axis. Scaling can be done by setting m11 and m22. For example, setting m11 to 2 and m22 to 1.5 will double the height and increase the width by 50%. The identity matrix has m11, m22, and m33 set to 1 (all others are set to 0) mapping a point to itself. Shearing is controlled by m12 and m21. Setting these elements to values different from zero will twist the coordinate system. Rotation is achieved by setting both the shearing factors and the scaling factors. Perspective transformation is achieved by setting both the projection factors and the scaling factors.

The following table is the combined transformations example using basic matrix operations.

void BasicOperations::paintEvent(QPaintEvent *)
{
double pi = 3.14;
double a = pi/180 * 45.0;
double sina = sin(a);
double cosa = cos(a);
QTransform translationTransform(1, 0, 0, 1, 50.0, 50.0);
QTransform rotationTransform(cosa, sina, -sina, cosa, 0, 0);
QTransform scalingTransform(0.5, 0, 0, 1.0, 0, 0);
QTransform transform;
transform = scalingTransform * rotationTransform * translationTransform;
QPainter painter(this);
painter.setPen(QPen(Qt::blue, 1, Qt::DashLine));
painter.drawRect(0, 0, 100, 100);
painter.setTransform(transform);
painter.setFont(QFont("Helvetica", 24));
painter.setPen(QPen(Qt::black, 1));
painter.drawText(20, 10, "QTransform");
}
See also
QPainter, Coordinate System

Member Enumeration Documentation

ConstantValue
QTransform::TxNone0x00
QTransform::TxTranslate0x01
QTransform::TxScale0x02
QTransform::TxRotate0x04
QTransform::TxShear0x08
QTransform::TxProject0x10

Constructor & Destructor Documentation

QTransform::QTransform ( )

Constructs an identity matrix. All elements are set to zero except m_11, m_22, and m_33 which are set to 1.

See also
reset()
QTransform::QTransform ( qreal  m11,
qreal  m12,
qreal  m13,
qreal  m21,
qreal  m22,
qreal  m23,
qreal  m31,
qreal  m32,
qreal  m33 = 1.0 
)

Constructs a matrix with the elements, m11, m12, m13, m21, m22, m23, m31, m32, m33.

See also
setMatrix()
QTransform::QTransform ( qreal  m11,
qreal  m12,
qreal  m21,
qreal  m22,
qreal  dx,
qreal  dy 
)

Constructs a matrix with the elements, m11, m12, m21, m22, dx and dy.

See also
setMatrix()
QTransform::QTransform ( const QMatrix matrix)
explicit

Constructs a matrix that is a copy of the given matrix. The values for m13, m23, and m33 are set to 0, 0, and 1 respectively.

Method Documentation

QTransform QTransform::adjoint ( ) const
nodiscard

Returns the adjoint of this matrix.

qreal QTransform::det ( ) const
inlinedeprecated
Deprecated:
Returns the matrix's determinant. Use determinant() instead.
qreal QTransform::determinant ( ) const
inline

Returns the matrix's determinant.

qreal QTransform::dx ( ) const
inline

Returns the horizontal translation factor.

See also
m31(), translate()
qreal QTransform::dy ( ) const
inline

Returns the vertical translation factor.

See also
translate()
QTransform QTransform::fromScale ( qreal  sx,
qreal  sy 
)
static

Creates a matrix which corresponds to a scaling of sx horizontally and sy vertically. This is equivalent to calling QTransform().scale(sx, sy) but slightly faster.

QTransform QTransform::fromTranslate ( qreal  dx,
qreal  dy 
)
static

Creates a matrix which corresponds to a translation of dx along the x axis and dy along the y axis. This is equivalent to calling QTransform().translate(dx, dy) but slightly faster.

QTransform QTransform::inverted ( bool *  invertible = nullptr) const
nodiscard

Returns an inverted copy of this matrix.

If the matrix is singular (not invertible), the returned matrix is the identity matrix. If invertible is valid (i.e. not 0), its value is set to true if the matrix is invertible, otherwise it is set to false.

See also
isInvertible()
bool QTransform::isAffine ( ) const
inline

Returns true if the matrix represent an affine transformation, otherwise returns false.

bool QTransform::isIdentity ( ) const
inline

Returns true if the matrix is the identity matrix, otherwise returns false.

See also
reset()
bool QTransform::isInvertible ( ) const
inline

Returns true if the matrix is invertible, otherwise returns false.

See also
inverted()
bool QTransform::isRotating ( ) const
inline

Returns true if the matrix represents some kind of a rotating transformation, otherwise returns false.

See also
reset()
bool QTransform::isScaling ( ) const
inline

Returns true if the matrix represents a scaling transformation, otherwise returns false.

See also
reset()
bool QTransform::isTranslating ( ) const
inline

Returns true if the matrix represents a translating transformation, otherwise returns false.

See also
reset()
qreal QTransform::m11 ( ) const
inline

Returns the horizontal scaling factor.

See also
scale()
qreal QTransform::m12 ( ) const
inline

Returns the vertical shearing factor.

See also
shear()
qreal QTransform::m13 ( ) const
inline

Returns the horizontal projection factor.

See also
translate()
qreal QTransform::m21 ( ) const
inline

Returns the horizontal shearing factor.

See also
shear()
qreal QTransform::m22 ( ) const
inline

Returns the vertical scaling factor.

See also
scale()
qreal QTransform::m23 ( ) const
inline

Returns the vertical projection factor.

See also
translate()
qreal QTransform::m31 ( ) const
inline

Returns the horizontal translation factor.

See also
dx(), translate()
qreal QTransform::m32 ( ) const
inline

Returns the vertical translation factor.

See also
dy(), translate()
qreal QTransform::m33 ( ) const
inline

Returns the division factor.

See also
translate()
QLine QTransform::map ( const QLine line) const

Creates and returns a QLineF object that is a copy of the given line mapped into the coordinate system defined by this matrix.

QLineF QTransform::map ( const QLineF line) const

Creates and returns a QLine object that is a copy of the given line, mapped into the coordinate system defined by this matrix. The transformed coordinates are rounded to the nearest integer.

QPainterPath QTransform::map ( const QPainterPath path) const

Creates and returns a QPainterPath object that is a copy of the given path, mapped into the coordinate system defined by this matrix.

QPoint QTransform::map ( const QPoint point) const

Creates and returns a QPoint object that is a copy of the given point, mapped into the coordinate system defined by this matrix. The transformed coordinates are rounded to the nearest integer.

QPointF QTransform::map ( const QPointF point) const

Creates and returns a QPointF object that is a copy of the given point mapped into the coordinate system defined by this matrix.

QPolygon QTransform::map ( const QPolygon polygon) const

Creates and returns a QPolygon object that is a copy of the given polygon, mapped into the coordinate system defined by this matrix. The transformed coordinates are rounded to the nearest integer.

QPolygonF QTransform::map ( const QPolygonF polygon) const

Creates and returns a QPolygonF object that is a copy of the given polygon, mapped into the coordinate system defined by this matrix.

QRegion QTransform::map ( const QRegion region) const

Creates and returns a QRegion object that is a copy of the given region, mapped into the coordinate system defined by this matrix. Calling this method can be rather expensive if rotations or shearing are used.

void QTransform::map ( int  x,
int  y,
int *  tx,
int *  ty 
) const

Maps the given coordinates x and y into the coordinate system defined by this matrix. The resulting values are put in tx and ty, respectively. The transformed coordinates are rounded to the nearest integer.

void QTransform::map ( qreal  x,
qreal  y,
qreal tx,
qreal ty 
) const

Maps the given coordinates x and y into the coordinate system defined by this matrix. The resulting values are put into tx and ty respectively.

The coordinates are transformed using the following formulas. The point (x, y) is the original point, and (x', y') is the transformed point.

x' = m11*x + m21*y + dx
y' = m22*y + m12*x + dy
if (is not affine) {
w' = m13*x + m23*y + m33
x' /= w'
y' /= w'
}
See also
Basic Matrix Operations
QRect QTransform::mapRect ( const QRect rect) const

Creates and returns a QRect object that is a copy of the given rect, mapped into the coordinate system defined by this matrix. The transformed coordinates are rounded to the nearest integer.

QRectF QTransform::mapRect ( const QRectF rect) const

Creates and returns a QRectF object that is a copy of the given rect, mapped into the coordinate system defined by this matrix. If rotation or shearing has been specified the bounding rectangle is returned. To retrieve the exact region the given rectangle maps to, call mapToPolygon() instead.

The rectangle's coordinates are transformed using the following formulas.

x' = m11*x + m21*y + dx
y' = m22*y + m12*x + dy
if (is not affine) {
w' = m13*x + m23*y + m33
x' /= w'
y' /= w'
}
See also
mapToPolygon()
QPolygon QTransform::mapToPolygon ( const QRect rect) const

Creates and returns a QPolygon representation of the given rect, mapped into the coordinate system defined by this matrix. Polygons and rectangles behave slightly differently when transformed (due to integer rounding). This means calling matrix.map(QPolygon(rect)) is not always the same as calling matrix.mapToPolygon(rect).

The rectangle's coordinates are transformed using the following formulas.

x' = m11*x + m21*y + dx
y' = m22*y + m12*x + dy
if (is not affine) {
w' = m13*x + m23*y + m33
x' /= w'
y' /= w'
}
See also
mapRect()
QTransform::operator QVariant ( ) const

Returns the transform as a QVariant.

bool QTransform::operator!= ( const QTransform &  transform) const

Returns true if this matrix is not equal to the given transform, otherwise returns false.

QTransform QTransform::operator* ( const QTransform &  transform) const

Returns the result of multiplying this matrix by the given transform. Matrix multiplication is not commutative, for example a*b != b*a.

QTransform & QTransform::operator*= ( const QTransform &  transform)

Returns the result of multiplying this matrix by the given transform.

QTransform & QTransform::operator*= ( qreal  factor)
inline

Returns the result of performing an element-wise multiplication of this matrix with the given factor.

QTransform & QTransform::operator+= ( qreal  delta)
inline

Returns the matrix obtained by adding the given delta to each element of this matrix.

QTransform & QTransform::operator-= ( qreal  delta)
inline

Returns the matrix obtained by subtracting the given delta from each element of this matrix.

QTransform & QTransform::operator/= ( qreal  factor)
inline

Returns the result of performing an element wise division of this matrix by the given factor.

QTransform & QTransform::operator= ( const QTransform &  other)

Copy assigns from other and returns a reference to this object.

bool QTransform::operator== ( const QTransform &  transform) const

Returns true if this matrix is equal to the given matrix, otherwise returns false.

bool QTransform::quadToQuad ( const QPolygonF quad1,
const QPolygonF quad2,
QTransform &  result 
)
static

Computes a transformation matrix which transforms the given quad1 to quad2. If this can be created the output will be placed in result and return value will be true. If no transformation can be created for the given quad the return value is false.

See also
squareToQuad(), quadToSquare()
bool QTransform::quadToSquare ( const QPolygonF quad,
QTransform &  result 
)
static

Computes a transformation matrix which transforms the given quad to a one unit square. If this can be created the output will be placed in result and return value will be true. If no transformation can be created for the given quad the return value is false.

See also
squareToQuad(), quadToQuad()
void QTransform::reset ( )

Resets the matrix to an identity matrix, i.e. all elements are set to zero, except m11 and m22 (specifying the scale) and m33 which are set to 1.

See also
QTransform(), isIdentity()
QTransform & QTransform::rotate ( qreal  angle,
Qt::Axis  axis = Qt::ZAxis 
)

Rotates the coordinate system counterclockwise by the given angle about the specified axis and returns a reference to the matrix. If you apply a QTransform to a point defined in widget coordinates, the direction of the rotation will be clockwise because the y-axis points downwards. The angle is specified in degrees.

See also
setMatrix()
QTransform & QTransform::rotateRadians ( qreal  angle,
Qt::Axis  axis = Qt::ZAxis 
)

Rotates the coordinate system counterclockwise by the given angle about the specified axis and returns a reference to the matrix. If you apply a QTransform to a point defined in widget coordinates, the direction of the rotation will be clockwise because the y-axis points downwards.

The angle is specified in radians.

See also
setMatrix()
QTransform & QTransform::scale ( qreal  sx,
qreal  sy 
)

Scales the coordinate system by sx horizontally and sy vertically, and returns a reference to the matrix.

See also
setMatrix()
void QTransform::setMatrix ( qreal  m11,
qreal  m12,
qreal  m13,
qreal  m21,
qreal  m22,
qreal  m23,
qreal  m31,
qreal  m32,
qreal  m33 
)

Sets the matrix elements to the specified values, m11, m12, m13 m21, m22, m23 m31, m32 and m33. This method replaces the previous values. QTransform provides the translate(), rotate(), scale() and shear() convenience functions to manipulate the various matrix elements based on the currently defined coordinate system.

See also
QTransform()
QTransform & QTransform::shear ( qreal  sh,
qreal  sv 
)

Shears the coordinate system by sh horizontally and sv vertically, and returns a reference to the matrix.

See also
setMatrix()
bool QTransform::squareToQuad ( const QPolygonF quad,
QTransform &  result 
)
static

Computes a transformation matrix which transforms a one unit square to the given quad. If this can be created the output will be placed in result and return value will be true. If no transformation can be created for the given quad the return value is false.

See also
quadToSquare(), quadToQuad()
const QMatrix & QTransform::toAffine ( ) const

Returns the current QTransform as an affine matrix.

Warning
If a perspective transformation has been specified, then the conversion will cause loss of data.
QTransform & QTransform::translate ( qreal  dx,
qreal  dy 
)

Moves the coordinate system dx along the x axis and dy along the y axis, and returns a reference to the matrix.

See also
setMatrix()
QTransform QTransform::transposed ( ) const
nodiscard

Returns the transpose of this matrix.

TransformationType QTransform::type ( ) const

Returns the transformation type of this matrix.

The transformation type is the highest enumeration value capturing all of the matrix's transformations. For example, if the matrix both scales and shears, the type would be TxShear, because TxShear has a higher enumeration value than TxScale.

Knowing the transformation type of a matrix is useful for optimization: you can often handle specific types more optimally than handling the generic case.

Friends And Related Function Documentation

QLine operator* ( const QLine line,
const QTransform &  matrix 
)
related

Equivalent to calling matrix.map(line).

See also
QTransform::map()
QLineF operator* ( const QLineF line,
const QTransform &  matrix 
)
related

Equivalent to calling matrix.map(line).

See also
QTransform::map()
QPainterPath operator* ( const QPainterPath path,
const QTransform &  matrix 
)
related

Equivalent to calling matrix.map(path).

See also
QTransform::map()
QPoint operator* ( const QPoint point,
const QTransform &  matrix 
)
related

Equivalent to calling matrix.map(point).

See also
QTransform::map()
QPointF operator* ( const QPointF point,
const QTransform &  matrix 
)
related

Equivalent to calling matrix.map(point).

See also
QTransform::map()
QPolygon operator* ( const QPolygon polygon,
const QTransform &  matrix 
)
related

Equivalent to calling matrix.map(polygon).

See also
QTransform::map()
QPolygonF operator* ( const QPolygonF polygon,
const QTransform &  matrix 
)
related

Equivalent to calling matrix.map(polygon).

See also
QTransform::map()
QRegion operator* ( const QRegion region,
const QTransform &  matrix 
)
related

Equivalent to calling matrix.map(region).

See also
QTransform::map()
QDataStream & operator<< ( QDataStream stream,
const QTransform &  matrix 
)
related

Writes the given matrix to the given stream and returns a reference to the stream.

See also
Refer to Serializing Data Types for additional information
QDataStream & operator>> ( QDataStream stream,
QTransform &  matrix 
)
related

Reads the given matrix from the given stream and returns a reference to the stream.

See also
Refer to Serializing Data Types for additional information
bool qFuzzyCompare ( const QTransform &  transform1,
const QTransform &  transform2 
)
related

Returns true if transform1 and transform2 are equal, allowing for a small fuzziness factor for floating point comparisons, false otherwise.

uint qHash ( const QTransform &  key,
uint  seed = 0 
)
related

Returns the hash value for key using seed to seed the calculation.